OR GATE

The OR gate produces a 1 if at least one input is 1.  Otherwise a 0 is produced.

Have a look...

Here is part of a truth table for the OR gate:-

x	y	Q = (x + y)
0	0	0
0

~Now try the activity~

Activity B

Fill in the rest of the OR truth table

    NOT GATE

The NOT gate inverts an input so a 1 becomes a 0 and a 0 becomes a 1.

Have a look...

Here is part of a truth table for the NOT gate:-

x	Q = ( x )
0
1

~Now try the activity~

Activity C

Fill in the rest of the NOT truth table

    NAND GATE

The NAND gate produces outputs the inverse of those for the AND gate.

Have a look...

Here is part of a truth table for the NAND gate:-

x	y	Q = (x.y)
0	0	1
0

~Now try the activity~

    NOR GATE

The NOR gate produces outputs the inverse of those for the OR gate

Have a look...

Here is part of a truth table for the NOR gate:-

x	y	Q = (x+y)
0	0	1
0

~Now try the activity~

Activity E

Fill in the rest of the NOR truth table

    XOR GATE

The XOR gate produces a 1 only if one input is 1.  Otherwise a 0 is produced.

Have a look...

Here is part of a truth table for the XOR gate:-

x	y	Q = (X.Y + X.Y)
0	0	0
0

~Now try the activity~

Combinations and Arithmetic

    Combining Logic Gates

Logic gates can be combined to form logic circuits.  Consider the combination of an OR gate and a NOT gate.

Here is part of a truth table for this circuit:-

A	B	A + B	A + B
0	0	0	1
0

~Now try the activity~

Activity G

Fill in the rest of the truth table above. Which logic function does the circuit simulate - AND, OR, NOT, NAND, NOR or XOR? Draw two logic gates that simulate a NAND gate.

    Binary Addition

How can we use logic gates to carry out computer arithmetic?

Let's suppose we wish to add two binary digits X and Y.  Considering  the following table:-

X	Y	Carry	Sum
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	0

When we add two binary digits, we may get the result of 00, 01, or 10.  We can consider the left bit to be a carry bit.  Now consider the 0's and 1's as two signals.  We require two input signals and two output signals.  I.e.

How can we use gates to construct this half-adder. Consider the following circuit:-

This circuit simulates the sum operation where the two inputs are 0 and the output is 0.

Can this circuit be used to simulate the other three sum operations?  Try the activity and find out.

~Now try the activity~

Exercises

Now try the following.

That's it!!